Question: Simplify; express your answer in exponential form. Assume $k\neq 0, r\neq 0$. $\dfrac{{k^{4}r^{-4}}}{{(k^{4}r^{-1})^{-4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${k^{4}r^{-4} = k^{4}r^{-4}}$ On the left, we have ${k^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${k^{4} = k^{4}}$ Apply the ideas above to simplify the equation. $\dfrac{{k^{4}r^{-4}}}{{(k^{4}r^{-1})^{-4}}} = \dfrac{{k^{4}r^{-4}}}{{k^{-16}r^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{4}r^{-4}}}{{k^{-16}r^{4}}} = \dfrac{{k^{4}}}{{k^{-16}}} \cdot \dfrac{{r^{-4}}}{{r^{4}}} = k^{{4} - {(-16)}} \cdot r^{{-4} - {4}} = k^{20}r^{-8}$